<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 14 (filtered medium)"><style><!--
/* Font Definitions */
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri","sans-serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
p.MsoPlainText, li.MsoPlainText, div.MsoPlainText
{mso-style-priority:99;
mso-style-link:"Plain Text Char";
margin:0in;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri","sans-serif";}
span.PlainTextChar
{mso-style-name:"Plain Text Char";
mso-style-priority:99;
mso-style-link:"Plain Text";
font-family:"Calibri","sans-serif";}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri","sans-serif";}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>-----Original Message-----<br>From: gsoc-porta-bounces@lists.r-forge.r-project.org [mailto:gsoc-porta-bounces@lists.r-forge.r-project.org] On Behalf Of Brian G. Peterson<br>Sent: Friday, October 04, 2013 12:59 PM<br>To: gsoc-porta@r-forge.wu-wien.ac.at<br>Subject: Re: [GSoC-PortA] Mean-mETL objective?</p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>If it is an LP problem, I think you can only minimize subject to constraints.<o:p></o:p></p><p class=MsoPlainText><b><i><span style='color:black'>[Doug] Although I have never check this, it does not sound right. The inner product in the LP formulation of ETL supports that formulation of ETL as an LP, but there should be no problem to adding another piece representing the inner product of mean return forecasts and portfolio weights (mean portfolio return estimate). I will check it out, as I had intended to add this in the ETL chapter.</span></i></b><span style='color:black'><o:p></o:p></span></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>If it is a QP problem, can't you do the mean/ETL portfolio?<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>That assumes the space is convex, which it will be for Gaussian ETL,<o:p></o:p></p><p class=MsoPlainText><b><i>[Doug] But that case is not interesting, does not add value relative to MVO.<o:p></o:p></i></b></p><p class=MsoPlainText><b><i><o:p> </o:p></i></b></p><p class=MsoPlainText> and may not be for modified Cornish Fisher ETL, but will be most of the time, at most reasonable confidence levels.<o:p></o:p></p><p class=MsoPlainText><b><i><span style='color:black'>[Doug] For both standard and modified ETL, the problem is in general non-convex. I guess you are saying from your experience the problem with modified ETL usually appears to be convex. I’m curious about how you ascertain that? E.g., because on multiple runs with DeOptim you seldom find more than one local minimum? That would certainly be reassuring.<o:p></o:p></span></i></b></p><p class=MsoPlainText><b><i><span style='color:black'><o:p> </o:p></span></i></b></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText>Brian<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>On 10/04/2013 02:42 PM, Ross Bennett wrote:<o:p></o:p></p><p class=MsoPlainText>> Peter,<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> Unfortunately, with ROI we are only able to minimize ETL with ETL as <o:p></o:p></p><p class=MsoPlainText>> an objective. If you have mean and ETL as an objective using ROI, <o:p></o:p></p><p class=MsoPlainText>> unless there is a target in the mean return objective, we just <o:p></o:p></p><p class=MsoPlainText>> minimize ETL. If you have both mean and ETL as objectives, you could <o:p></o:p></p><p class=MsoPlainText>> add a target to the mean objective and this will minimize ETL subject to the target return.<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> We can do the following with ETL as an objective using ROI:<o:p></o:p></p><p class=MsoPlainText>> - Minimize ETL subject to leverage, box, group, exposure, position <o:p></o:p></p><p class=MsoPlainText>> limit, and target return.<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> Multipliers are ignored with ROI since the problems are formulated <o:p></o:p></p><p class=MsoPlainText>> into an LP/QP problem. I'll take a look at the documentation in <o:p></o:p></p><p class=MsoPlainText>> optimize.portfolio and make sure this is clear.<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> I hope that helps clear it up.<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> Ross<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> On Fri, Oct 4, 2013 at 11:49 AM, Peter Carl <peter@braverock.com <o:p></o:p></p><p class=MsoPlainText>> <<a href="mailto:peter@braverock.com"><span style='color:windowtext;text-decoration:none'>mailto:peter@braverock.com</span></a>>> wrote:<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> Hey Ross,<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> I can't seem to get the Mean-mETL objective to select anything other<o:p></o:p></p><p class=MsoPlainText>> than<o:p></o:p></p><p class=MsoPlainText>> the Min mETL portfolio using ROI. It looks like there should be good<o:p></o:p></p><p class=MsoPlainText>> convexity, but I think there's a substantial imbalance between the<o:p></o:p></p><p class=MsoPlainText>> size of<o:p></o:p></p><p class=MsoPlainText>> the monthly mean return and the loss indicated by the ETL. I've tried<o:p></o:p></p><p class=MsoPlainText>> modifying the multiplier on the mean, but it doesn't seem to have an<o:p></o:p></p><p class=MsoPlainText>> effect.<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> Any thoughts?<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> pcc<o:p></o:p></p><p class=MsoPlainText>_______________________________________________<o:p></o:p></p><p class=MsoPlainText>GSoC-PortA mailing list<o:p></o:p></p><p class=MsoPlainText><a href="mailto:GSoC-PortA@lists.r-forge.r-project.org"><span style='color:windowtext;text-decoration:none'>GSoC-PortA@lists.r-forge.r-project.org</span></a><o:p></o:p></p><p class=MsoPlainText><a href="http://lists.r-forge.r-project.org/cgi-bin/mailman/listinfo/gsoc-porta"><span style='color:windowtext;text-decoration:none'>http://lists.r-forge.r-project.org/cgi-bin/mailman/listinfo/gsoc-porta</span></a><o:p></o:p></p></div></body></html>